Visualization of 3D coupled vibration in drill bits

ABSTRACT

Drill bit vibration data for lateral, axial, and torsional directions of a drill bit is collected for a simulated or deployed drill bit for visualization of 3D coupled vibration. A frequency converter transforms the drill bit vibration data into frequency vibration data. A drill bit analyzer identifies local maxima (“peaks”) in the frequency vibration data in each of the lateral, axial, and torsional directions. Common peaks across all 3 directions with sufficiently high frequency and sufficiently high bit rotation speed are indicated as 3D coupled vibration. A drill bit data visualizer uses the indications of 3D coupled vibration in addition to the vibration data and frequency vibration data to generate visualizations of 3D coupled vibration in the drill bit.

BACKGROUND

The disclosure generally relates to earth or rock drilling and todrilling tools.

Deployed drill bits experience vibrations in the axial, lateral, andtorsional directions downhole that generate wear over time. In additionto vibrations along individual directions, such as high frequencytorsional oscillation (HFTO) in the torsional direction, vibrationscouple across multiple dimensions. 2D coupled vibrations include coupledvibrations of a drillstring including coupled axial-torsionalvibrations, coupled axial-lateral vibrations and coupledtorsional-lateral vibrations.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the disclosure may be better understood by referencing theaccompanying drawings.

FIG. 1 is a schematic diagram of a drill bit data visualizer forvisualizing 3D coupled vibration in a drill bit.

FIG. 2 is a schematic diagram of a drill bit designer for mitigating 3Dcoupled vibration.

FIG. 3 is a flowchart of example operations for visualizing vibrationdata for a drill bit.

FIG. 4 is a flowchart of example operations for designing a drill bitwith reduced 3D coupled vibration.

FIG. 5 is a flowchart of example operations for detecting 3D coupledvibration for a drill bit.

FIG. 6 is a flowchart of example operations for generating drill bitdesigns.

FIG. 7 depicts an example computer system with drill bit data visualizerand a drill bit design generator.

FIG. 8 is a diagram of a polycrystalline diamond compact (PDC) bithaving an embedded accelerometer.

FIG. 9 depicts plots of vibrational data and vibrational frequency datafor a PDC drill bit experiencing 3D coupled vibration.

FIG. 10 depicts plots of vibrational data and vibrational frequency datafor a 9⅞″, 6 blade PDC drill bit experiencing 3D coupled vibration.

FIG. 11 depicts plots of vibrational data and vibrational frequency datafor an 8½″, 6 blade PDC drill bit experiencing 3D coupled vibration.

FIG. 12 depicts plots of vibrational data and vibrational frequency datafor a 8½″, 5 blade PDC drill bit experiencing 3D coupled vibration.

FIG. 13 depicts plots of vibrational data and vibrational frequency datafor a 8½″, 7 blade PDC drill bit experiencing 3D coupled vibration.

FIG. 14 depicts a plot of drilling efficiency (DE) in percent versus bitside cutting efficiency (SCE) in percent for non-directional PDC bitswith bit size in the range 6.125 inches to 8.75 inches.

FIG. 15 depicts a plot of bit drilling efficiency (DE) in percent versusbit side cutting efficiency (SCE) in percent for non-directional PDCbits with bit size in the range 9.775 inches to 17.5 inches.

FIG. 16 depicts a plot of bit drilling efficiency (DE) in percent versusbit side cutting efficiency (SCE) in percent for directional bits withbit size between 6.75 inches and 8.75 inches.

FIG. 17 depicts plots of spectrograms for vibrational drill bit data.

FIG. 18 depicts a plot of various drilling parameters versus time in adrilling operation.

DESCRIPTION

The description that follows includes example systems, methods,techniques, and program flows that embody aspects of the disclosure.However, it is understood that this disclosure may be practiced withoutthese specific details. For instance, this disclosure refers tovisualizing drill bit data for drill bits to detect 3D coupled vibrationin illustrative examples. Aspects of this disclosure can be insteadapplied to visualizing drill bit data to detect vibration in other typesof drillstring or sub-assembly components. In other instances,well-known instruction instances, protocols, structures, and techniqueshave not been shown in detail in order not to obfuscate the description.

Overview

When vibration occurs within a drill bit at the same frequency acrossall 3 of the lateral, axial, and torsional directions relative to thedrill bit, the vibrations can amplify each other to create resonance ina bottom hole assembly. This “3D coupled vibration” can substantiallyamplify wear in both the drill bit and the entire bottom hole assembly.A drill bit visualizer for visualizing and detecting 3D coupledvibration in polycrystalline diamond compact (PDC) drill bits isdisclosed herein. Drill bit vibrational data corresponding to lateral,axial, and torsional vibration in either a deployed or simulated drillbit is aggregated over time or depth windows for a drilling operation. Afrequency converter converts the drill bit vibrational data intofrequency vibrational data corresponding to frequency spectra for theaxial, lateral, and torsional vibrations. A vibrational data analyzerdetermines local maxima (“peaks”) in the amplitude of the frequency dataacross windows of time and further detects 3D coupled vibration ascommon peaks across vibration directions with sufficiently highfrequency and rotational speed. From the detected 3D coupled vibrationand vibrational/frequency data, the vibrational data analyzer generatesvisualizations for the frequency data, such as spectrograms of frequencyamplitude versus time or depth for each of the lateral, torsional, andaxial vibrations, visualizations of peak amplitudes in a frequencyversus time or depth graph, and visual indicators of the presence of 3Dcoupled vibration. The vibrational data analyzer communicates thevisualizations along with indications of 3D coupled vibration forfurther analysis.

Example Illustrations

FIG. 1 is a schematic diagram of a drill bit data visualizer forvisualizing 3D coupled vibration in a drill bit. Drilling of oil and gaswells is commonly carried out using a string of drill pipes connectedtogether so as to form a drilling string 108 that is lowered through arotary table 110 into a wellbore or borehole 112 in a well 106. Thedrill string 108 may operate to pass through the rotary table 110 fordrilling the borehole 112 through subsurface formations 114. The drillstring 108 may include a drill pipe 118 and a bottom hole assembly 120,perhaps located at the lower portion of the drill pipe 118. The bottomhole assembly 120 includes drill collars 122, a down hole tool 124, anda drill bit 126. The drill bit 126 operates to create a borehole 112 bypenetrating a surface 104 and subsurface formations 114. The down holetool 124 may comprise any of a number of different types of toolsincluding MWD tools, LWD tools, and others.

During drilling operations, the drill string 108 (perhaps including thedrill pipe 118 and the bottom hole assembly 120) may be rotated by therotary table 110. In addition to, or alternatively, the bottom holeassembly 120 may also be rotated by a motor (e.g., a mud motor) that islocated down hole. The drill collars 122 may be used to add weight tothe drill bit 126. The drill collars 122 may also operate to stiffen thebottom hole assembly 120, allowing the bottom hole assembly 120 totransfer the added weight to the drill bit 126, and in turn, to assistthe drill bit 126 in penetrating the surface 104 and subsurfaceformations 114. A vibrational sensor 130 (e.g., a gyroscope) is embeddedin the axial shaft of the drill bit 126 and can detect high frequencyvibrational data for the drill bit 126 in the axial, torsional, andlateral directions. Typical frequencies for vibration detection can bebetween 0 and 400 hertz (Hz). Additional vibrational sensors can besituated throughout the bottom hole assembly 120 to detect vibrationspropagating beyond just the drill bit 126. Often in the case of 3Dcoupled vibration, vibrations occurring in the drill bit 126 can inducevibrations in the entire bottom hole assembly 120 which increases wearon its components and may damage some of them.

A computer 102 situated at the surface 104 collects drill bitvibrational data 101 from the vibrational sensor 130 downhole. Thecomputer 102 can be communicatively coupled to the vibrational sensor130 via, for instance, a wire running down the drill string 108.Although depicted as at the surface 104, the computer 102 can be runningoffsite or can be collecting drill bit vibrational data 101 from asimulated drill bit in a lab prior to deployment. The computer 102comprises a drill bit data visualizer 100 that converts the drill bitvibrational data 101 into frequency data in order to visualize anddetect 3D coupled vibration.

A frequency converter 132 running on the drill bit data visualizer 100receives the drill bit vibrational data 101. The frequency converter 132converts the drill bit vibrational data 101 into frequency vibrationdata 103. For instance, the frequency converter 132 can apply a discreteFourier transform to the drill bit vibrational data 101 for each of theaxial, lateral, and vibrational directions. The Fourier transformationcan be applied to windows of time or depth or can be applied globallyacross all values of time or depth. If {t_(i)}^(n) _(i=1) are timevalues at which to compute the Fourier transform, and {r_(i)}^(n) _(i=1)are the corresponding values for rotational speed in revolutions perminute (RPMs), then the j-th coefficient for the torsional frequencyspectrum ω_(j,T) can be computed using the discrete Fourier transform asω_(j,T)=Σ^(n) _(i=1)r_(i)e^(−i2π/nj(i-1)). The frequency vibrationaldata 103 comprises the values of these coefficients across all values ofj=1, . . . , n as well as for varying windows for computing the Fouriertransform. For the lateral and axial vibrations, the RPM values can bereplaced by lateral amplitude and axial amplitude respectively (in g orgravitational force in meters per second squared). Instead of using adiscrete Fourier transform, embodiments could use a continuous Fouriertransform, various types of wavelet transforms, band pass filters, etc.to determine the frequency vibrational data 103.

A vibrational data analyzer 134 receives the frequency vibrational data103 comprising frequency spectrums for the lateral, torsional, and axialvibrational data in the drill bit vibrational data 101 over variouswindows. The vibrational data analyzer 134 analyzes the frequencyspectrums (i.e. absolute values of coefficients of the discrete Fouriertransform) to determine the top k peaks in frequency spectrum for eachof the windows and determines the presence of 3D coupled vibration basedon common peaks across the frequency spectrums for each of thetorsional, vibrational, and lateral frequency data. The value for k canvary across windows and can be determined based on prior experiments indetecting 3D coupled vibration or known domain knowledge about typicalnumbers of peaks for the frequency spectrums. The vibrational dataanalyzer 134 aggregates data for frequency spectrums and 3D coupledvibration to generate visualizations including a drill bit vibrationspectrogram 105. The visualizations include spectrograms, plots offrequency spectrums, plots of vibration, plots of 3D coupled vibrationon a graph of frequency versus depth, etc. either globally or foraggregated windows. For the drill bit vibration spectrogram 105, thevibrational data analyzer 134 collects data across evenly spaced windowsof time or depth (e.g., every 5 seconds) and plots the magnitude ofcoefficients in the frequency spectrum over each window. The shade ofeach rectangle in the drill bit vibration spectrogram 105 represents themagnitude of the corresponding coefficient, where the x-axis is time andthe y-axis is frequency. Alternatively, the spectrogram can plot thex-axis as frequency and the y-axis as time.

FIG. 2 is a schematic diagram of a drill bit design for mitigating 3Dcoupled vibration. FIG. 2 is annotated with a series of letters A-E.These letters represent stages of operations. Although these stages areordered for this example, the stages illustrate one example to aid inunderstanding this disclosure and should not be used to limit theclaims. Subject matter falling within the scope of the claims can varywith respect to the order and some of the operations.

A drill bit design generator 200 generates initial drill bit designs 201comprising various drill bit parameters 209 and sends the initial drillbit designs 201 to a drill bit simulator 202. The drill bit simulator202 determines drilling efficiency (DE) and side cutting efficiency(SCE) over a number of simulations for each bit design in the initialdrill bit designs 201. The drill bit simulator then sends simulateddrill bit data 205 from the simulations to a 3D coupled vibrationcorrelation analyzer 204. The 3D coupled vibration correlation analyzer204 determines whether 3D coupled vibration occurs using vibrationaldata for each of the simulations. The 3D coupled vibration correlationanalyzer 204 then correlates DE and SCE to 3D coupled vibration in thedrill bit designs and determines DE and SCE thresholds to mitigate 3Dcoupled vibration if such a correlation exists. The 3D coupled vibrationcorrelation analyzer 204 can further generate a plot 213 of DE versusSCE for 3D coupled and non-3D coupled drill bit designs. The plot 213can indicate a threshold for at least one of DE and SCE. The thresholdscan comprise a value or range of values, and a value can correspond toan upper or lower limit for a metric. The 3D coupled vibrationcorrelation analyzer 204 sends the drill bit design thresholds 207 tothe drill bit design generator 200. The drill bit design generator 200uses the drill bit design thresholds 207 to generate revised drill bitdesigns 203 which it sends to a drill bit manufacturer 206.

At stage A, the drill bit design generator 200 determines the set ofinitial drill bit designs 201. Each drill bit design has designparameters 209 which may include number of blades, blade orientation(directional, non-directional), bit size, bit shape, depth of cutcontrollers, back rake/side rake angles, gauge pad aggressiveness, etc.The initial drill bit designs 201 are determined based on operationalparameters of the expected deployment for the drill bits. For instance,for a directional drilling operation, the blade orientation can be moreconducive to the drill bit changing directions. Other parameters candepend on the weight on bit (WOB), compressive strength of the expectedrock types, and other ambient operational conditions such as temperatureand pressure downhole.

At stage B, the drill bit simulator 202 receives the initial drill bitdesigns 201 from the drill bit design generator 200. The drill bitsimulator 202 then runs simulations for each of the designs to determineDE and SCE for that design in addition to collecting vibrational data inthe torsional, lateral, and axial directions. The simulations can beconducted using a bottom hole assembly in a lab that drills throughartificially created rock formations resembling rock formations at adesired drill bit deployment location. Alternatively, the simulationscan be conducted at a real-world rock formation to simulate a bitdesign. The drill bits can have gyroscopic sensors and accelerometersinstalled in their axial shafts that can take high frequencymeasurements of axial, torsional, and lateral vibrations in the drillbit. During the simulations, the drill bit simulator 202 takes ongoingmeasurements of rate of penetration (ROP), rock compressive strength,cross-sectional area of the hole drilled by the bit, the torque on bit(TOB), rate of lateral penetration (ROL), and various forces tocalculate the total DE and SCE. The DE is computed asDE=σrock/E _(s)100%, where E _(s)=WOB/A+120π*RPM*TOB/A*ROP,  (1)and the SCE is computed asSCE=ROL/F _(s)/ROP/WOB100%,  (2)where σ_(rock) is the compressive strength of the rock in psi, A is thecross sectional area of the hole drilled by the bit, TOB is the torqueon bit, and F_(s) is the bit steer force. F_(s), WOB, and TOB can all becomputed based on the measured values for σ_(rock), RPM, ROP, and ROL.The drill bit simulator 202 sends the simulated drill bit data 205comprising the computed DE and SCE for each simulation as well as theother measurements taken during the simulation to the 3D coupledvibration correlation analyzer 204.

At stage C, the 3D coupled vibration correlation analyzer 204 detects 3Dcoupled vibration in the simulated drill bit data 205 and determines acorrelation between 3D coupled vibration and DE/SCE across simulations.This correlation can be determined, for instance, using mean squarederror for a simple linear regression on DE versus the presence of 3Dcoupled vibration (i.e. a linear regression with the binary responsevariable that indicates the presence of 3D coupled vibration). If themean squared error is below a threshold mean squared error, then thecorrelation can be determined to be present, and the 3D coupledvibration correlation analyzer 204 can determine a threshold value forDE/SCE. The threshold value is typically chosen as the maximal value ofDE/SCE for which a simulated drill bit experiences 3D coupled vibration.In some embodiments, outliers can be removed before determining thethreshold, and the threshold can be chosen using other methods.

The 3D coupled vibration correlation analyzer 204 can additionallygenerate a plot 213 of DE versus SCE for drill bit designs where 3Dcoupled vibration occurred and did not occur. The plot 213 is for atotal of 97 drill bit designs for which 20 drill bit designs experienced3D coupled vibration. The drill bit designs were all chosen to have abit size between 6.125 and 8.75 inches. Often drill bit designs withsimilar design considerations (e.g. bit size) are simulated together andthe correlation between DE/SCE and 3D coupled vibration is onlydetermined for the set of drill bit designs among the initial drill bitdesigns 201 with similar design considerations. For example, for plot213, the 3D coupled vibration correlation analyzer 204 determined thatthere was a correlation between DE and 3D coupled vibration and thethreshold was chosen to be the maximal DE of a drill bit design with 3Dcoupled vibration at around 43%. 97 runs of PDC bit deployments withnon-directional bit design with bit size between 6.124 inches and 8.75inches were conducted, of which 20 runs experienced 3D coupledvibration. For safety, the threshold DE can be chosen to be 45% toreduce the chance of 3D coupled vibration. Conversely, no correlationbetween SCE and 3D coupled vibration was found, and no threshold for SCEwas generated. The drill bit simulator 202 can track other (auxiliary)drill bit metrics and these auxiliary metrics can be correlated to 3Dcoupled vibration in addition or alternatively to DE and SCE.

At stage C, the drill bit design generator 200 receives the drill bitdesign threshold 207 generated by the 3D coupled vibration correlationanalyzer 204 and uses it to generate revised drill bit designs 203. Thedrill bit design generator 200 has prior knowledge about the DE and SCEfor certain drill bit designs and can select the drill bit parameters209 to ensure that the resulting drill bit exceeds desired DE and SCEthresholds upon implementation. In some embodiments, the drill bitdesign generator 200 can determine that the drill bit design thresholds207 do not permit a functional drill bit design for the desiredimplementation. In response, the drill bit design generator 200 canincrementally adjust one or more of the drill bit design thresholds 207until a drill bit design within the thresholds is possible.Additionally, the drill bit design generator 200 can send the reviseddrill bit designs 203 to the drill bit simulator 202 to verify theresulting drill bits do not experience 3D coupled vibrations using theoperations at stages A and B.

At stage D, the drill bit manufacturer 206 receives the revised drillbit designs 203 from the drill bit design generator 200. The drill bitmanufacturer 206 can generate drill bits that include gyroscope sensorsand accelerometers in the axial shaft to monitor 3D coupled vibration indeployed drill bits. If the deployed drill bits based on the reviseddrill bit designs 203 still experience frequent 3D coupled vibration orexperience wear after a low number of deployments, the drill bitmanufacturer 206 can query the drill bit design generator 200 for morestringent drill bit designs with possibly stricter design thresholds.

The example operations in FIGS. 3-6 are described with reference to adrill bit data visualizer, a drill bit design generator, and a drill bitanalyzer for consistency with the earlier figures. The name chosen forthe program code is not to be limiting on the claims. Structure andorganization of a program can vary due to platform, programmer/architectpreferences, programming language, etc. In addition, names of code units(programs, modules, methods, functions, etc.) can vary for the samereasons and can be arbitrary.

FIG. 3 is a flowchart of example operations for visualizing vibrationdata for a drill bit. At block 301, a drill bit data visualizer detects3D coupled vibration in drill bit data for a drill bit. Detecting 3Dcoupled vibration involves converting vibrational data for the drill bitinto frequency/amplitude vibrational data and analyzing thefrequency/amplitude vibrational data to determine common peaks fortorsional, lateral, and axial frequencies indicating 3D coupledvibration. These operations are described in greater detail with respectto FIG. 5 .

At block 303, the drill bit data visualizer aggregatesfrequency/amplitude vibrational data across drill bit data windows. Thedata can be aggregated across evenly spaced windows of time or depth inthe case of visualizing a spectrogram. Alternatively, the data can beaggregated globally across all time or depth values or can be aggregatedlocally in windows around times or depths where 3D coupled vibration isdetected at block 301. Aggregating the frequency/amplitude vibrationaldata can comprise averaging the data over blocks. Alternatively, otherstatistics such as standard deviation can be computed. Vibrational datafor the drill bit can additionally be aggregated for subsequentvisualization.

At block 305, the drill bit visualizer generates plots of axial,torsional, and lateral vibration data and aggregated frequency/amplitudevibrational data versus time and depth. The plots can includevibrational data versus time or depth, frequency amplitude versusfrequency, and/or heat maps of locations of 3D coupled vibration for thecorresponding windows of frequency, time, depth, etc. for each of theaxial, lateral, and torsional directions. The plots can includestatistics related to any of the aforementioned data sets and can be forany of the windows aggregated at block 303.

At block 307, the drill bit visualizer generates spectrograms offrequency vibration data versus time and depth using the frequency andamplitude vibrational data over time or depth windows. Each spectrogramcovers a set of windows in time or depth and comprises a heat map ofamplitude for an x-axis of time or depth and a y-axis of frequency. Adarker color in the heat map corresponds to a greater amplitude.Spectrograms can be generated independently for each of the torsional,lateral, and axial directions or can be generated across more than onedirection by averaging amplitudes.

At block 309, the drilling bit visualizer displays the plots andindicators generated at blocks 305, and 307. The plots can comprise alegend and axis labels. The plots can additionally comprise visualindicators of the presence of 3D coupled vibration such as dotted lines,arrows, markers, etc. Statistical information about the drill bit datathat is relevant to 3D coupled vibration, such as bit rotational speedat a peak frequency, can be displayed.

FIG. 4 is a flowchart of example operations for designing a drill bitwith reduced 3D coupled vibration. At block 401, a drill bit designgenerator determines a set of design thresholds for various designparameters and iteratively generates bit designs. If there areinsufficient bit designs within the set of design thresholds, the drillbit design generator relaxes the thresholds. The operations for bitdesign with reduced 3D coupled vibration are described in greater detailwith respect to FIG. 6 .

At block 403, the drill bit design generator begins iterating throughthe drill bit designs generated at block 401. The iterations comprisethe example operations at blocks 405, 407, and 409.

At block 405, the drill bit design generator simulates the drill bitdesign of the current iteration and collects vibrational drill bit datain the axial, lateral, and torsional directions. The drill bit designgenerator collects operational data from simulating the drill bit designto compute an efficiency metric for the drilling operation. Examples ofthe operational data include rate of penetration (ROP), rock compressivestrength, cross-sectional area of the hole drilled by the bit, andtorque on bit (TOB). The simulation can occur in a lab using a syntheticrock formation and a testing bottom hole assembly. Embodiments can useoperational data from a real-world drilling operation for simulating adesign. Embodiments can deploy a drill bit representative of multipledesigns in a real-world drilling operation and collect the operationaldata from sensors in the representative drill bit for simulations of therepresented drill bit designs. Numerical simulations of PDC bit-rockinteraction can be performed under specific drilling conditions for RPM,ROP, ROL, rock compressive strength, etc. Forces on each cutting elementand non-cutting element, as well as WOB, TOB, DE and SCE can becalculated by the simulator.

At block 407, the drill bit design generator detects 3D coupledvibration in the drill bit data simulated at block 405. Detecting 3Dcoupled vibration involves generating frequency vibrational data fromthe drill bit vibrational data simulated at block 405 then detectingcommon peak frequencies in the frequency vibrational data across thetorsional, lateral, and axial directions. The operations for detecting3D coupled vibration in drill bit data are described in further detailwith respect to FIG. 5 .

At block 409, the drill bit design generator determines drillingefficiency (DE) and side cutting efficiency (SCE) for the drill bitsimulation at block 405. DE and SCE can be determined using themeasurements for ROP, rock compressive strength, cross-sectional area ofthe hole drilled by the bit, and TOB taken at block 405 according toequations (1) and (2). Other efficiency or drilling metrics can becomputed, and wear on the bit before and after the simulation can betracked to gauge the wear effects of drill bit designs both with andwithout the presence of 3D coupled vibration.

At block 411, the drill bit design generator determines whether there isan additional drill bit design. If an additional drill bit designexists, operations return to block 403. Otherwise, operations continueto block 413.

At block 413, the drill bit design generator determines a correlationbetween DE and 3D coupled vibration and a correlation between SCE and 3Dcoupled vibration for all the bit designs iterated at blocks 403, 405,407, 409, and 411. Each correlation can be determined using a meansquared error for a regression model with the presence of 3D coupledvibration as a binary response variable as described above. More complexcorrelation techniques, including regression models with multiple designmetrics beyond DE and SCE can be used.

At block 415, the drill bit design generator checks whether acorrelation between DE and 3D coupled vibration or between SCE and 3Dcoupled vibration was determined at block 413. If such a correlation wasdetermined for either DE or SCE, operations continue to block 417.Otherwise, operations in FIG. 4 terminate.

At block 417, the drill bit design generator determines a threshold DEand/or SCE to reduce 3D coupled vibration using the determinedcorrelation(s). For each correlation, a threshold DE or SCE isdetermined over which 3D coupled vibration rarely occurs. The thresholdcan be determined as the maximal DE or SCE for which 3D coupledvibration is detected during simulations. Alternatively, an additionalbuffer can be added to the maximal DE or SCE to further reduce thechance of 3D coupled vibration. Alternative methods for determining thethreshold, including prior outlier removal upper threshold values, andranges of threshold values can be used.

At block 419, the drill bit design generator generates updated and/ornew drill bit designs using additional design considerations based onthe thresholds determined at block 417. The updated drill bit designscan be updated based on the original drill bit designs and the new drillbit designs can be generated from scratch using the thresholds for drillbit design parameters and simulated drill bit data. Any combination ofnew and updated drill bit designs can be implemented. These updatedand/or new drill bit designs are simulated or deployed to test for 3Dcoupled vibration. Drill bits designs can be simulated using operationaldata from a real-world deployment. Additionally or alternatively,representative drill bits can be deployed to collect sensor data toevaluate multiple drill bit designs associated with the representativedrill bit. Existing drill bit designs that are far outside of thresholdsfor drill bit design parameters can be removed and replaced with new bitdesigns. In some embodiments, updated drill bit designs within thethreshold DE or SCE will not be possible such that they still maintaindrill bit functionality during drilling operations. The thresholds canthus be relaxed so that updated drill designs can be generated.

At block 423, the drill bit design generator determines whether there isreduced 3D coupled vibration in the new/updated drill bit designssimulated or deployed at block 419. This determination can be based ondetection of 3D coupled vibration in the simulated/deployed drill bitdata as described with reference to block 407. If there is reduced 3Dcoupled vibration in the updated drill bit designs at a desired level ofreduction (e.g., 10% of tested drill bit designs), operations in FIG. 4terminate. Otherwise, operations continue to block 425.

At block 425, the drill bit design generator updates the drill bitdesign thresholds to further reduce 3D coupled vibration. For instance,the DE and/or SCE thresholds can be increased by an incremental amountto reduce the chance of 3D coupled vibration. In some embodiments,updating the drill bit thresholds while still enabling a feasible drillbit design for deployment is not possible. In these embodiments,operations at FIG. 4 terminate.

FIG. 5 is a flowchart of example operations for detecting 3D coupledvibration for a drill bit. At block 501, a drill bit analyzer collectstorsional, axial, and lateral vibration data for a drill bit. The drillbit analyzer can collect the data during simulations or deployment ofthe drill bit on a bottom hole assembly for a rock formation. The drillbit has an embedded accelerometer that can measure high-frequencyvibrational data in each of the aforementioned directions.

At block 503, the drill bit analyzer begins iterating over windows in aset of time or depth windows for drill bit data. The windows can bepredetermined based on a desired granularity of analysis, desiredvisualizations for the vibration data, etc. When only the detection ofthe presence of 3D coupled vibration is required, a single global windowover time or depth can be used. The iterations comprise the operationsat blocks 505, 507, 509, and 511.

At block 505, the drill bit analyzer determines a frequency andcorresponding amplitude for each of torsional, axial, and lateralvibration data over the window at the current iteration. The drill bitanalyzer can average and/or otherwise aggregate the vibration data forthe current window for each direction. Subsequently, the drill bitanalyzer can take a frequency transformation such as a discrete orcontinuous Fourier/Wavelet transform, a set of band pass filters, etc.The drill bit analyzer can take absolute values of any complex valuedspectrums resulting from these transformations.

At block 507, the drill bit analyzer determines a set of the top K localmaxima (“peaks”) in amplitude as a function of frequency within thecurrent window for each of the lateral, axial, and torsionalfrequency/amplitude vibration data. The local maxima are defined asamplitudes that have a higher value than every amplitude within asufficiently large neighborhood. The size of these neighborhoods and thevalue for K can depend on typical frequency statistics for spectra ofdrill bit vibration data (e.g., a common number of peaks in thevibration data for specific drill bit designs). Ranking the peaks can bedetermined by the prominence of each peak or a different metric (e.g., avalue of the discrete second derivative at each peak). Additionally, aminimum prominence requirement can be imposed to qualify as a peak sothat there may be less than K peaks.

At block 509, the drill bit analyzer determines whether there is 3Dcoupled vibration indicated in the top K peaks determined at block 507.3D coupled vibration is determined by the three following conditionsoccurring simultaneously:

-   -   (i—) a peak occurs at a frequency higher than 5 Hz        simultaneously for axial, lateral, and torsional vibration    -   (ii—) there is significant variation in RPM of the drill bit (in        the torsional direction) determined by the equation        max(RPM)−mean(RPM)/mean(RPM)>1 where the maximum and mean RPM        are determined over the current window (i.e. the RPM exceeds a        significant variation threshold) and    -   (iii—) the RPM at the dominant frequency is greater than 40 RPM        (i.e. the RPM at the dominant frequency exceeds a minimum RPM        threshold).

The latter 2 conditions are present in high-frequency torsionaloscillation (HFTO). Therefore, 3D coupled vibration includes HFTO whichis usually associated with a torsional resonance. 3D coupled vibrationmay be associated either with an axial harmonics resonance and/or with atorsional resonance. As a result, 3D coupled vibration is more harmfulthan HFTO, which amplifies each of the individual vibrations. The values5 Hz and 40 RPM and the equation for determining significant variationare examples and any thresholds or functions can vary. If the drill bitanalyzer determines the presence of 3D coupled vibration, operationscontinue to block 511. Otherwise, operations skip to block 513.

At block 511, the drill bit analyzer indicates the presence of 3Dcoupled vibration with corresponding window of depth/time and frequency.In some embodiments, the 3D coupled vibration can occur at multiplehigher resonant frequencies that are multiples of a base resonantfrequency. The indicator can alternatively only include a binaryindicator that 3D coupled vibration occurred.

At block 513, the drill bit analyzer checks for an additional window inthe set of time/depth windows. If there is an additional window,operations return to block 503. Otherwise, operations in FIG. 5terminate.

FIG. 6 is a flowchart of example operations for generating drill bitdesigns. At block 601, a drill bit design generator determines a set ofthresholds for drill bit design parameters corresponding to a desireddrill bit design. There can be a wide array of possible drill bit designparameters including number of blades, blade orientation, bit size, bitshape, depth of cut controllers, back rake/side rake angles, gauge padaggressiveness, etc. that can depend on operational designconsiderations such as whether a drilling system is directional,weight-on-bit, torque-on-bit, rate of penetration etc.

At block 603, the drill bit design generator begins iterating over eachdrill bit design threshold in the set of drill bit design thresholdsdetermined at block 601. Operations at each iteration include block 605.

At block 605, the drill bit design generator narrows the set of totalfeasible drill bit designs based on the drill bit design threshold atthe current iteration. The drill bit design threshold can correspond tothreshold values for certain drill bit design parameters or cancorrespond to thresholds for a function of drill bit design parameters.For instance, for DE or SCE, the drill bit designs are constrained by afunction that ensures the drill bit design will have sufficiently highDE or SCE. The drill bit parameters can be measured by a function of allor a subset of the parameters and an upper or lower threshold to theseparameters can be imposed to improve DE, SCE, or an auxiliary metric ofdrill bit performance. The drill bit design generator can discardfeasible drill bit designs by computing one or more functions of thedrill bit parameters and discarding designs with function values aboveor below a threshold function value. The number of remaining bit designscan be reduced to zero at block 605, and in response, operations canskip to block 611. Otherwise, operations continue to block 607.

At block 607, the drill bit design generator determines if there is anadditional drill bit design threshold. If an additional drill bit designthreshold exists, operations return to block 603. Otherwise, operationscontinue to block 609.

At block 609, the drill bit design generator determines whether thenumber of remaining drill bit designs is greater than a desired numberof drill bit designs. The desired number of drill bit designs can be aminimum number of drill bit designs to simulate to ensure conditions aremet that were enforced by the drill bit design thresholds e.g., thatthere is a reduced frequency of 3D coupled vibration. If there is asufficiently high number of drill bit designs, operations skip to block613. Otherwise, operations continue to block 611.

At block 611, the drill bit design generator relaxes at least one of thedrill bit design thresholds. When a drill bit design threshold is athreshold for one or more drill bit design parameters, the drill bitdesign generator can increase or decrease the drill bit designthresholds based on whether they are upper or lower thresholds.Alternatively, when the drill bit design threshold is a function ofmultiple drill bit design parameters, the drill bit design generator candetermine an upper or lower threshold for the function. Operationsreturn to block 603.

At block 613, the drill bit design generator returns the remaining drillbit designs. The drill bit design generator can additionally return thedrill bit design thresholds and an indication of whether the drill bitdesign thresholds were relaxed during the operations of FIG. 6 .

The flowcharts are provided to aid in understanding the illustrationsand are not to be used to limit scope of the claims. The flowchartsdepict example operations that can vary within the scope of the claims.Additional operations may be performed; fewer operations may beperformed; the operations may be performed in parallel; and theoperations may be performed in a different order. For example, theoperations depicted in blocks 407 and 409 can be performed in parallelor concurrently. With respect to FIG. 5 , multiple windows of timeand/or depth are not necessary. It will be understood that each block ofthe flowchart illustrations and/or block diagrams, and combinations ofblocks in the flowchart illustrations and/or block diagrams, can beimplemented by program code. The program code may be provided to aprocessor of a general-purpose computer, special purpose computer, orother programmable machine or apparatus.

FIG. 7 depicts an example computer system with a drill bit datavisualizer and a drill bit design generator. The computer systemincludes a processor 701 (possibly including multiple processors,multiple cores, multiple nodes, and/or implementing multi-threading,etc.). The computer system includes memory 707. The memory 707 may besystem memory or any one or more of the above already described possiblerealizations of machine-readable media. The computer system alsoincludes a bus 703 and a network interface 705. The system also includesa drill bit data visualizer 711 and a drill bit design generator 713.The drill bit data visualizer 711 can convert lateral, axial, andtorsional vibration data for a drill bit into frequency vibration data,can detect 3D coupled vibration in the frequency vibration data, and cangenerate visualization and indications of the vibration data, frequencyvibration data, and presence of 3D coupled vibration. The drill bitdesign generator 713 can determine drill bit designs within operationalthresholds, can test the drill bit designs for 3D coupled vibration aswell as drilling efficiency (DE) and side cutting efficiency (SCE), candetermine correlations between DE and/or SCE and 3D coupled vibration,and can update the drill bit design based on the determined correlationbetween DE and/or SCE and 3D coupled vibration. Any one of thepreviously described functionalities may be partially (or entirely)implemented in hardware and/or on the processor 701. For example, thefunctionality may be implemented with an application specific integratedcircuit, in logic implemented in the processor 701, in a co-processor ona peripheral device or card, etc. Further, realizations may includefewer or additional components not illustrated in FIG. 7 (e.g., videocards, audio cards, additional network interfaces, peripheral devices,etc.). The processor 701 and the network interface 705 are coupled tothe bus 703. Although illustrated as being coupled to the bus 703, thememory 707 may be coupled to the processor 701.

FIG. 8 is a diagram of a PDC bit having an embedded accelerometer. A PDCbit 800 comprises cutting blades 803A, 803B, 803C, and 803D, eachcutting blade comprising cutters such as cutters 805A, 805B, 805C, 805D,etc. that are embedded on cutting blade 803A. The PDC bit 800 furthercomprises an accelerometer 801 embedded in an axial shaft. Theaccelerometer 801 can comprise any sensor configured to measurevibrations of the PDC bit 800 in the axial, lateral, and torsionaldirections downhole (e.g., a gyroscope). The PDC bit 800 can vary withrespect to the number of cutters, number of cutting blades, and anydesign parameters including blade orientation, bit size, bit shape, etc.The PDC bit 800 is configured to make high frequency vibrationalmeasurements during simulation or deployment.

FIG. 9 depicts plots of vibrational data and vibrational frequency datafor a PDC drill bit experiencing 3D coupled vibration. A plot 901displays axial vibration in a z direction in g (acceleration due togravity) versus drilling time in seconds. A plot 903 displays lateralvibration in an x direction in g versus drilling time in seconds. A plot905 displays bit rotational speed in RPM versus drilling time inseconds. The overall average bit rotational speed is 139.4967 RPM. Plots907, 909, and 911 display frequency in Hz versus an axial, lateral, andtorsional frequency spectrum, respectively. In each plot, the only peakfrequency is at 36.6588 Hz. At this frequency, the axial and lateralvibration amplitudes are 0.08 g and 0.9 g respectively, and the bitrotational speed is 95 RPM. There is a common peak frequency that isgreater than 5 Hz, significant variation in RPM, and bit rotationalspeed above 40 RPM at the peak frequency. These three factors combinedindicate the presence of 3D coupled vibration.

FIG. 10 depicts plots of vibrational data and vibrational frequency datafor a 9⅞″, 6 blade PDC drill bit experiencing 3D coupled vibration.Plots 1001, 1003, and 1005 display axial, lateral, and torsionalvibration in g, g, and RPM respectively versus time in seconds. Plots1007, 1009, and 1001 display plots of lateral, torsional, and frequencyspectrum, respectively, versus frequency in Hz. All plots are for thePDC drill bit depicted with top view 1013 and side view 1015 having bitsize 9⅞″ with 6 blades that is a non-directional PDC drill bit deployedin a vertical well. A primary frequency for 3D coupled vibration occursat ω₁=38.94 Hz. A second harmonics response occurs in all threevibrations at double the primary frequency, ω₂=77.88 Hz. Excitation ofhigher axial harmonics occurs in the BHA at frequencies of 120.5 Hz,156.7 Hz, 195.6 Hz, 234.6 Hz, and 273.5 Hz.

FIG. 11 depicts plots of vibrational data and vibrational frequency datafor an 8½″, 6 blade PDC drill bit experiencing 3D coupled vibration.Plots 1101, 1103, and 1105 display axial, lateral, and torsionalvibration in g, g, and RPM respectively versus time in seconds. Plots1107, 1109, and 1111 display plots of lateral, torsional, and frequencyspectrum respectively versus frequency in Hz. All plots are for the PDCdrill bit depicted with top view 1113 and side view 1115 having bit size8½″ with 6 blades deployed in a directional well by a push-the-bitrotary steerable system tool. The coupled frequency for 3D coupledvibration occurs at 269.8 Hz. A primary frequency of 134.4 Hz occurredin the axial and lateral vibrations, but not in torsional vibration.Lower order torsional peak frequencies occur at 57.4 Hz and 155.1 Hz,and a higher torsional peak frequency occurs at 302.37 Hz. Higher orderaxial harmonics can be correlated with non-directional bits, as seen inthe following table which demonstrates a higher relative rate of axialharmonics specifically for PDC bits exhibiting 3D coupled vibration:

Non-Directional Bits Design With Full Without Full Directional FeaturesGauge Gauge Bits Total Runs Number of Bit 71 91 84 246 Runs % Having 3D20(28%) 15(16%) 12(14%) 47(19%) Coupled Vibration Relative % 19(95%)12(80%)  8(67%) 39(83%) Having Axial Harmonics

FIG. 12 depicts plots of vibrational data and vibrational frequency datafor an 8½″, 5 blade PDC drill bit experiencing 3D coupled vibration.Plots 1201, 1203, and 1205 display axial, lateral, and torsionalvibration in g, g, and RPM respectively versus time in seconds. Plots1207, 1209, and 1201 display plots of lateral, torsional, and frequencyspectrum respectively versus frequency in Hz. All plots are for the PDCdrill bit depicted with top view 1213 and side view 1215 having bit size8½″ with 5 blades in directional drilling with a motor. Lateral andtorsional vibrations are dominated by the frequency 185.67 Hz. Thelateral vibration amplitude at this frequency is around 11 g and the bitrotational speed is 90 RPM. The axial vibrations do not exhibitharmonics, but the frequency spectrum is distributed with three peaksnear 102 Hz, 182 Hz, and 307 Hz. Torsional vibrations occur with peaksat 44.05 Hz, 120.6 Hz, 185.67 Hz, and 207 Hz. The peak in the axialfrequency spectrum around 182 Hz is enough to induce 3D coupledvibration.

FIG. 13 depicts plots of vibrational data and vibrational frequency datafor a 8½″, 7 blade PDC drill bit experiencing 3D coupled vibration.Plots 1301, 1303, and 1305 display axial, lateral, and torsionalvibration in g, g, and RPM respectively versus time in seconds. Plots1307, 1309, and 1301 display plots of lateral, torsional, and frequencyspectrum respectively versus frequency in Hz. All plots are for the PDCdrill bit depicted with top view 1313 and side view 1315 having bit size8½″ with 7 blades in directional drilling with a push-the-bit rotarysteerable system. 3D coupled vibration occurs at 397.74 Hz whichdominates the lateral vibration. Axial and lateral vibrations arecoupled at 132.58 Hz, 265.2 Hz, and 397.7 Hz. Conversely, the torsionalvibrations exhibit peaks at 132.58 Hz and 291.1 Hz.

FIG. 14 depicts a plot of bit drilling efficiency (DE) in percent versusbit side cutting efficiency (SCE) in percent for non-directional PDCbits with bit size in the range 6.125 inches to 8.75 inches. In the plot1400, 97 runs (i.e. 97 PDC bit deployments) were conducted with 20occurrences of 3D coupled vibration. Several of the occurrences of both3D coupled vibration and no 3D coupled vibration occurred with the sameDE/SCE values and are represented as a single icon in FIG. 14 . Allinstances of 3D coupled vibration occurred at DE<44%. Therefore, designconsiderations include a threshold DE>44%. Conversely, no correlationbetween SCE and 3D coupled vibration was detected and therefore this isnot a factor in design considerations.

FIG. 15 depicts a plot of bit drilling efficiency (DE) in percent versusbit side cutting efficiency (SCE) in percent for non-directional PDCbits with bit size in the range 9.875 inches to 17.5 inches. In the plot1500, 65 runs (i.e. 65 PDC bit deployments) were conducted with 15occurrences of 3D coupled vibration. Several of the occurrences of both3D coupled vibration and no 3D coupled vibration occurred with the sameDE/SCE values and are represented as a single icon in FIG. 15 . Allinstances of 3D coupled vibration occurred at DE<29% and SCE<5%.Therefore, design considerations include a threshold DE>30% and athreshold SCE>5% as depicted in the plot 1500.

FIG. 16 depicts a plot of bit drilling efficiency (DE) in percent versusbit side cutting efficiency (SCE) in percent for directional bits withbit size between 6.75 inches and 8.75 inches. In the plot 1600, 73 runs(i.e. 73 deployments of PDC bits) were conducted with 11 occurrences of3D coupled vibration. Several of the occurrences of both 3D coupledvibration and no 3D coupled vibration occurred with the same DE/SCEvalues and are represented as a single icon in FIG. 16 . All instancesof 3D coupled vibration occurred at DE<45% and SCE<5%. Therefore, designconsiderations include a threshold DE>45% and a threshold SCE>5% asdepicted in the plot 1600.

FIG. 17 depicts plots of spectrograms for vibrational drill bit data.Plot 1701 depicts a heat map of amplitude in g over a plot of frequencyin Hz versus depth in feet. Frequency ranges from 0 Hz to 357.14 Hz,depth ranges in even intervals from around 9329 feet to 11772 feet, andamplitude ranges from 0 g to 0.316 g. Artifacts in the form of verticallight-colored stripes occur throughout the spectrogram representing thebeginning of drilling operations at higher depths and the periodicpausing of drilling operations at lower depths. Interspersed with thevertical light-colored lines are dark horizontal bands representing highamplitude frequencies, possibly indicating 3D coupled vibration whencorrelated with frequency data for other directions. Plot 1703 depicts aheat map of amplitude in G over a plot of frequency in Hz versus depthin feet. Frequency ranges from 0 Hz to 357.14 Hz, time ranges in evenintervals from around April 19th, 11:28 to May 3, 12:31, and amplituderanges from 0 g to 0.316 g. Similar light-colored vertical stripes occurto those present in plot 1701. Additionally, dark colored horizontalbands representing high amplitude frequencies can be compared to highamplitude frequencies in other directions to detect 3D coupledvibration.

FIG. 18 depicts a plot of various drilling parameters versus time in adrilling operation. A plot 1801 plots time on the Y axis betweenapproximately 7:30 and 9:00 versus drilling parameters comprisingtemperature, average vibration in X, Y, and Z directions, peak vibrationin X, Y, and Z directions, min RPM, average RPM, max RMP, and 3D coupledvibration. To the far right in plot 1801, temperature is plotted inFahrenheit and remains close to 200° F. at all times. To the right oftemperature is average vibration in g in each of the X, Y, and Zdirections representing lateral, torsional, and axial vibrations,respectively. Average vibrations remain relatively uniform across alldirections, with vibrations in the X and Y directions maintaining aconsistent higher magnitude, and periodic lulls in amplitudecorresponding to interruptions in drilling operations. To the right ofaverage vibrations are peak vibrations in g in each of the X, Y, Zdirections. The peak vibrations exhibit similar behavior to the averagevibrations. To the right of peak vibrations are minimum, maximum, andaverage rotational speed in RPMs. Predictably, the minimum rotationalspeed is consistently lower than the average rotational speed, which isalso consistently lower than the maximum rotational speed. Spikes in allof the rotational speeds occur prior to the peaks in 3D coupledvibration at around 7:45, 8:20, and 8:45.

As will be appreciated, aspects of the disclosure may be embodied as asystem, method or program code/instructions stored in one or moremachine-readable media. Accordingly, aspects may take the form ofhardware, software (including firmware, resident software, micro-code,etc.), or a combination of software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”The functionality presented as individual modules/units in the exampleillustrations can be organized differently in accordance with any one ofplatform (operating system and/or hardware), application ecosystem,interfaces, programmer preferences, programming language, administratorpreferences, etc.

Any combination of one or more machine-readable medium(s) may beutilized. The machine-readable medium may be a machine-readable signalmedium or a machine-readable storage medium. A machine-readable storagemedium may be, for example, but not limited to, a system, apparatus, ordevice, that employs any one of or combination of electronic, magnetic,optical, electromagnetic, infrared, or semiconductor technology to storeprogram code. More specific examples (a non-exhaustive list) of themachine-readable storage medium would include the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a portable compact disc read-only memory (CD-ROM), anoptical storage device, a magnetic storage device, or any suitablecombination of the foregoing. In the context of this document, amachine-readable storage medium may be any tangible medium that cancontain or store a program for use by or in connection with aninstruction execution system, apparatus, or device. A machine-readablestorage medium is not a machine-readable signal medium.

A machine-readable signal medium may include a propagated data signalwith machine-readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Amachine-readable signal medium may be any machine-readable medium thatis not a machine-readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a machine-readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

The program code/instructions may also be stored in a machine-readablemedium that can direct a machine to function in a particular manner,such that the instructions stored in the machine-readable medium producean article of manufacture including instructions which implement thefunction/act specified in the flowchart and/or block diagram block orblocks.

While the aspects of the disclosure are described with reference tovarious implementations and exploitations, it will be understood thatthese aspects are illustrative and that the scope of the claims is notlimited to them. In general, techniques for detecting 3D coupledvibration using common peaks in frequency vibrational data acrosslateral, axial, and torsional directions in a drill bit, visualizing the3D coupled vibration, and correlating drilling efficiency and sidecutting efficiency to inform drill bit design as described herein may beimplemented with facilities consistent with any hardware system orhardware systems. Many variations, modifications, additions, andimprovements are possible.

Plural instances may be provided for components, operations orstructures described herein as a single instance. Finally, boundariesbetween various components, operations and data stores are somewhatarbitrary, and particular operations are illustrated in the context ofspecific illustrative configurations. Other allocations of functionalityare envisioned and may fall within the scope of the disclosure. Ingeneral, structures and functionality presented as separate componentsin the example configurations may be implemented as a combined structureor component. Similarly, structures and functionality presented as asingle component may be implemented as separate components. These andother variations, modifications, additions, and improvements may fallwithin the scope of the disclosure.

As used herein, the term “or” is inclusive unless otherwise explicitlynoted. Thus, the phrase “at least one of A, B, or C” is satisfied by anyelement from the set {A, B, C} or any combination thereof, includingmultiples of any element.

Example Embodiments

Embodiment 1: a method comprising applying a frequency transformation tovibrational data for a drill bit to generate frequency vibrational datafor the drill bit, wherein the vibrational data for the drill bitcomprises vibrational data in lateral, axial, and torsional directionsrelative to the drill bit, identifying a plurality of frequency peaks inthe frequency vibrational data, wherein the plurality of frequency peaksis determined based, at least in part, on local maxima in the frequencyvibrational data for each direction, determining whether at least afirst frequency corresponds to a peak for each of the directions in theplurality of frequency peaks, and based, at least in part, on adetermination that the first frequency corresponds to a peak for each ofthe directions, indicating occurrence of 3D coupled vibration in thedrill bit at the first frequency.

Embodiment 2: the method of Embodiment 1, further comprising determiningwhether revolutions per minute data in the vibrational data is above adefined significant variation threshold, and determining whetherrevolutions per minute data in the vibrational data at the firstfrequency satisfies a defined minimum revolutions per minute threshold.

Embodiment 3: the method of any of Embodiments 1-2, wherein thecorresponding frequencies for the plurality of frequency peaks in thefrequency vibrational data are above a defined minimum frequency.

Embodiment 4: the method of any of Embodiments 1-3, wherein thefrequency transformation is applied to a plurality of time or depthwindows for the vibrational data.

Embodiment 5: the method of Embodiment 4, wherein the local maxima areidentified within a time or depth window in the plurality of time ordepth windows.

Embodiment 6: the method of any of Embodiments 1-5, further comprisingdisplaying an indication of 3D coupled vibration in the drill bit at thefirst frequency.

Embodiment 7: the method of any of Embodiments 1-6, further comprisinggenerating a spectrogram of the frequency vibrational data for each ofthe lateral, axial, and torsional directions.

Embodiment 8: the method of any of Embodiments 1-7, further comprisinggenerating plots of the frequency vibrational data for each of thelateral, axial, and torsional directions.

Embodiment 9: a non-transitory, machine-readable medium havinginstructions stored thereon that are executable by a computing device toperform operations comprising identifying local amplitude maxima infrequency domain vibration data for each of multiple directions relativeto a drill bit, wherein the multiple directions include axial,torsional, and lateral directions, determining whether resonance occursat a common frequency of a subset of the local amplitude maxima acrossthe directions in a first window of the frequency domain vibration data,determining whether high-frequency torsional oscillation occurs in thefirst window, based on a determination that the resonance andhigh-frequency torsional oscillation occurs in the first window,indicating detection of 3-dimensional coupled vibration at the commonfrequency.

Embodiment 10: the non-transitory, machine-readable medium of Embodiment9, wherein determining whether resonance occurs at a common frequency ofa subset of the local amplitude maxima across the directions in a firstwindow comprises determining whether the local amplitude maximum in thefirst window for each of the directions at the common frequency isgreater than a defined minimum resonance frequency.

Embodiment 11: the non-transitory, machine-readable medium of any ofEmbodiments 9-10, wherein determining whether high-frequency torsionaloscillation occurs in the first window comprises determining whetherrevolutions per minute data across the first window exceeds a definedsignificant variation threshold, and determining whether revolutions perminute datum in the first window at the common frequency satisfies adefined minimum revolutions per minute threshold.

Embodiment 12: the non-transitory, machine-readable medium of any ofEmbodiments 9-11 having further instructions stored thereon that areexecutable by a computing device to perform operations comprising, foreach of the directions, aggregating the vibration data of the directionwithin the first window and then applying a frequency transformation tothe aggregated vibration data to generate the frequency domain vibrationdata.

Embodiment 13: an apparatus comprising a processor, and acomputer-readable medium having instructions stored thereon that areexecutable by the processor to cause the apparatus to apply a frequencytransformation to vibrational data for a drill bit to generate frequencyvibrational data for the drill bit, wherein the vibrational data for thedrill bit comprises vibrational data in lateral, axial, and torsionaldirections relative to the drill bit, identify a plurality of frequencypeaks in the frequency vibrational data, wherein the plurality offrequency peaks is determined based, at least in part, on local maximain the frequency vibrational data for each direction, determine whetherat least a first frequency corresponds to a peak for each of thedirections in the plurality of frequency peaks, and based, at least inpart, on a determination that the first frequency corresponds to a peakfor each of the directions, indicate occurrence of 3D coupled vibrationin the drill bit at the first frequency.

Embodiment 14: the apparatus of Embodiment 13, further comprisinginstructions executable by the processor to cause the apparatus todetermine whether revolutions per minute data in the vibrational data isabove a defined significant variation threshold, and determine whetherrevolutions per minute data in the vibrational data at the firstfrequency satisfies a defined minimum revolutions per minute threshold.

Embodiment 15: the apparatus of any of Embodiments 13-14, wherein thecorresponding frequencies for the plurality of frequency peaks in thefrequency vibrational data are above a defined minimum frequency.

Embodiment 16: the apparatus of any of Embodiments 13-15, wherein thefrequency transformation is applied to a plurality of time or depthwindows for the vibrational data.

Embodiment 17: the apparatus of Embodiment 16, wherein the local maximaare identified within a time or depth window in the plurality of time ordepth windows.

Embodiment 18: the apparatus of any of Embodiments 13-17, furthercomprising instructions executable by the processor to cause theapparatus to display an indication of 3D coupled vibration in the drillbit at the first frequency.

Embodiment 19: the apparatus of any of Embodiments 13-18, furthercomprising generating a spectrogram of the frequency vibrational datafor each of the lateral, axial, and torsional directions.

Embodiment 20: the apparatus of any of Embodiments 13-19, furthercomprising generating plots of the frequency vibrational data for eachof the lateral, axial, and torsional directions.

The invention claimed is:
 1. A method comprising: applying a frequencytransformation to vibrational data for a drill bit to generate frequencyvibrational data for the drill bit, wherein the vibrational data for thedrill bit comprises vibrational data in lateral, axial, and torsionaldirections relative to the drill bit; identifying a plurality offrequency peaks in the frequency vibrational data, wherein the pluralityof frequency peaks is determined based, at least in part, on localmaxima in the frequency vibrational data for each direction; determiningwhether at least a first frequency corresponds to a peak for each of thedirections in the plurality of frequency peaks; and based, at least inpart, on a determination that the first frequency corresponds to a peakfor each of the directions, indicating occurrence of 3D coupledvibration in the drill bit at the first frequency.
 2. The method ofclaim 1, further comprising: determining whether revolutions per minutedata in the vibrational data is above a defined significant variationthreshold; and determining whether revolutions per minute data in thevibrational data at the first frequency satisfies a defined minimumrevolutions per minute threshold.
 3. The method of claim 1, wherein thecorresponding frequencies for the plurality of frequency peaks in thefrequency vibrational data are above a defined minimum frequency.
 4. Themethod of claim 1, wherein the frequency transformation is applied to aplurality of time or depth windows for the vibrational data.
 5. Themethod of claim 4, wherein the local maxima are identified within a timeor depth window in the plurality of time or depth windows.
 6. The methodof claim 1, further comprising displaying an indication of 3D coupledvibration in the drill bit at the first frequency.
 7. The method ofclaim 1, further comprising generating a spectrogram of the frequencyvibrational data for each of the lateral, axial, and torsionaldirections.
 8. The method of claim 1, further comprising generatingplots of the frequency vibrational data for each of the lateral, axial,and torsional directions.
 9. A non-transitory, machine-readable mediumhaving instructions stored thereon that are executable by a computingdevice to perform operations comprising: identifying local amplitudemaxima in frequency domain vibration data for each of multipledirections relative to a drill bit, wherein the multiple directionsinclude axial, torsional, and lateral directions; determining whetherresonance occurs at a common frequency of a subset of the localamplitude maxima across the directions in a first window of thefrequency domain vibration data; determining whether high-frequencytorsional oscillation occurs in the first window; based on adetermination that the resonance and high-frequency torsionaloscillation occurs in the first window, indicating detection of3-dimensional coupled vibration at the common frequency.
 10. Thenon-transitory, machine-readable medium of claim 9, wherein determiningwhether resonance occurs at a common frequency of a subset of the localamplitude maxima across the directions in a first window comprisesdetermining whether the local amplitude maximum in the first window foreach of the directions at the common frequency is greater than a definedminimum resonance frequency.
 11. The non-transitory, machine-readablemedium of claim 9, wherein determining whether high-frequency torsionaloscillation occurs in the first window comprises: determining whetherrevolutions per minute data across the first window exceeds a definedsignificant variation threshold; and determining whether revolutions perminute datum in the first window at the common frequency satisfies adefined minimum revolutions per minute threshold.
 12. Thenon-transitory, machine-readable medium of claim 9 having furtherinstructions stored thereon that are executable by a computing device toperform operations comprising, for each of the directions, aggregatingthe vibration data of the direction within the first window and thenapplying a frequency transformation to the aggregated vibration data togenerate the frequency domain vibration data.
 13. An apparatuscomprising: a processor; and a computer-readable medium havinginstructions stored thereon that are executable by the processor tocause the apparatus to, apply a frequency transformation to vibrationaldata for a drill bit to generate frequency vibrational data for thedrill bit, wherein the vibrational data for the drill bit comprisesvibrational data in lateral, axial, and torsional directions relative tothe drill bit; identify a plurality of frequency peaks in the frequencyvibrational data, wherein the plurality of frequency peaks is determinedbased, at least in part, on local maxima in the frequency vibrationaldata for each direction; determine whether at least a first frequencycorresponds to a peak for each of the directions in the plurality offrequency peaks; and based, at least in part, on a determination thatthe first frequency corresponds to a peak for each of the directions,indicate occurrence of 3D coupled vibration in the drill bit at thefirst frequency.
 14. The apparatus of claim 13, further comprisinginstructions executable by the processor to cause the apparatus to:determine whether revolutions per minute data in the vibrational data isabove a defined significant variation threshold; and determine whetherrevolutions per minute data in the vibrational data at the firstfrequency satisfies a defined minimum revolutions per minute threshold.15. The apparatus of claim 13, wherein the corresponding frequencies forthe plurality of frequency peaks in the frequency vibrational data areabove a defined minimum frequency.
 16. The apparatus of claim 13,wherein the frequency transformation is applied to a plurality of timeor depth windows for the vibrational data.
 17. The apparatus of claim16, wherein the local maxima are identified within a time or depthwindow in the plurality of time or depth windows.
 18. The apparatus ofclaim 13, further comprising instructions executable by the processor tocause the apparatus to display an indication of 3D coupled vibration inthe drill bit at the first frequency.
 19. The apparatus of claim 13,further comprising generating a spectrogram of the frequency vibrationaldata for each of the lateral, axial, and torsional directions.
 20. Theapparatus of claim 13, further comprising generating plots of thefrequency vibrational data for each of the lateral, axial, and torsionaldirections.